We consider the exploration-exploitation dilemma in finite-horizon reinforcement learning (RL). When the state space is large or continuous, traditional tabular approaches are unfeasible and some form of function approximation is mandatory. In this paper, we introduce an optimistically-initialized variant of the popular randomized least-squares value iteration (RLSVI), a model-free algorithm where exploration is induced by perturbing the least-squares approximation of the action-value function. Under the assumption that the Markov decision process has low-rank transition dynamics, we prove that the frequentist regret of RLSVI is upper-bounded by $\widetilde O(d^2 H^2 \sqrt{T})$ where $ d $ are the feature dimension, $ H $ is the horizon, and $ T $ is the total number of steps. To the best of our knowledge, this is the first frequentist regret analysis for randomized exploration with function approximation.

翻译：我们考虑有限时域强化学习中的探索-利用困境。当状态空间较大或连续时，传统的表格化方法难以实现，必须采用某种形式的函数逼近。本文引入了一种乐观初始化的流行随机化最小二乘值迭代变体，这是一种无模型算法，通过扰动动作价值函数的最小二乘逼近来诱导探索。在假设马尔可夫决策过程具有低秩转移动态的条件下，我们证明了随机化最小二乘值迭代的频域遗憾上界为$\widetilde O(d^2 H^2 \sqrt{T})$，其中$d$为特征维度，$H$为时域长度，$T$为总步数。据我们所知，这是针对函数逼近下随机化探索的首个频域遗憾分析。